This invention relates to cascaded optical waveguides and, more particularly, to mutually coupled waveguide arrays.
The star coupler, which divides the power entering over any of its input ports among its output ports, is used to interconnect waveguide arrays. Different messages can be communicated among the various subscribers by using wavelength, or time division multiplexing. C. Dragone in U.S. Pat. No. 4,904,042 issued to the assignee of the present application, teaches that, especially for single mode waveguides, the star coupler""s input and output waveguides should be arranged in circular arrays and that the center of curvature of the arc segment of the input array should lie on the arc segment of the output array, and vice versa. Also, the axes of the waveguides in each array should be directed to the center of curvature of the arc defining the configuration of that array and the radius of the circles defining the configuration of each array should be chosen to maximize the transmission from the marginal input elements to the marginal output elements. The aperture of each of the elements may be further varied from element to element to maximize the efficiency of the array. The coupler is typically designed so that the optical radiation entering the coupler is confined, by fabricating layers of appropriately doped silica, to a two-dimensional silica slab of low loss material. Power transfer between the input and output ports of the coupler takes place in a free space region defined by a slab waveguide between two arrays of waveguides. Power entering any of the waveguides excites the dominant mode of the waveguide, is radiated in the coupler region and is intercepted by the receiving array aperture.
In order to achieve high efficiency of power transfer between a relatively large number of input ports and a relatively large number of output ports and a small star-coupler physical size, the input and output waveguides connected to the star coupler must be relatively narrow and be closely spaced at the star coupler. However close spacing gives rise to significant mutual coupling between adjacent waveguides, leading to undesirable crosstalk between the channels of the device. C. Dragone in U.S. Pat. No. 5,136,671 has shown that by locating the foci of the respective input and output arrays at a predetermined distance away from and outside the free space region (e.g., of the slab) and appropriately adjusting the star-coupler waveguide lengths to minimize residual aberrations, phase errors and cross-talk caused by mutual coupling between the waveguides may be minimized. Specifically, the focal point of each array should be located so that it coincides with the phase center of the other array and that residual phase errors may be reduced by appropriately setting the lengths of the waveguides in the optical grating between two star couplers. See also the article entitled xe2x80x9cOptimum Design of a Planar Array of Tapered Waveguidesxe2x80x9d, J. Opt. Soc. Am. A. vol. 7, pp 2081-2093, 1990.
While moving the convergence points of the waveguides off the free space boundaries and into the waveguide array partially compensates for the mutual coupling phase distortion, this physical distortion of the star coupler generally results in the star coupler no longer acting as a discrete Fourier transformer. Thus, to preserve the Fourier transform functionality of the star coupler and its benefits, such as facilitating the design process and speeding and simplifying the design simulation, one should keep the conventional coupler geometry in which the convergence point of each array falls on the termination point of the center waveguide of the next array. Instead one should adjust the waveguide lengths. Note, that for very strong mutual coupling, where the field changes significantly over angle changes on the order of {square root over (2+L /kR))}, star coupler physical distortions can no longer be avoided.
Consider, for instance, a waveguide router, consisting of a waveguide grating placed between two arrays. In this case the grating is effectively located in the far field of either array. Mutual coupling that gives rise to phase distortion also distorts the transmission coefficients of the router. It would be extremely advantageous, especially in waveguides used in interferometric devices, such as waveguide grating routers and waveguide lenses, to compensate for mutual coupling phase distortion without having to change coupler geometry.
When a lightwave is sent into a single port on one side of a star coupler, the lightwaves that appear in the ports on the other side will not have the same phase if there is mutual coupling among the waveguides. Such mutual coupling arises among the waveguides where they are closely spaced near the free space region at the edges of the slab. We have discovered that the phase distortion is approximately periodic and may be compensated for by adding or subtracting length to the waveguides between the star couplers. The path length correction is essentially a sinusoid with the minimum increase in required path length being applicable to the ports at the centers of the star-coupler Brillouin zones and the maximum increase in required length being applicable to the ports at the edges of the star-coupler Brillouin zones. The magnitude of the sinusoid can be found by numerical beam propagation in the waveguide array. The angular period of the distortion is given by xcex/a, where xcex is the free-space region wavelength and a is the center to center waveguide spacing at the edge of the free space region. We have also discovered that by eliminating phase distortions, a star coupler accurately performs a proper Fourier transformation so that when two star couplers are cascaded so as to perform two Fourier transformations without phase distortions, an imaging arrangement results which accurately reproduces at the output the input distribution.